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Translation in cylindrically symmetric vacuum

  • M.-N. Célérier
  • R. ChanEmail author
  • M. F. A. da Silva
  • N. O. Santos
Research Article
  • 25 Downloads

Abstract

Starting from the stationary cylindrically symmetric solution, but with the coordinates z and \(\phi \) interchanged, and supposing that it could describe the vacuum spacetime of a translating cylinder, we investigate its physical and geometrical properties. This hypothesis is not entirely new since it has already been considered in a previous paper describing a translating source. We show that this metric is geometrically related to the vacuum field produced by a stationary rotating cylindrical source, known as Lewis solution. However, we find new physical properties, different from those of the Lewis vacuum solution. Moreover, we show that no translating cylindrical dust solution can exist in general relativity.

Notes

Acknowledgements

Financial assistance from FAPERJ/UERJ (MFAdaS) is gratefully acknowledged. The author (RC) acknowledges financial support from FAPERJ (Nos. E-26/171.754/2000, E-26/171.533/2002, E-26/170.951/2006, E-26/110.432/2009 and E26/111.714/2010). The authors (RC and MFAdaS) also acknowledge financial support from Conselho Nacional de Desenvolvimento Científico e Tecnológico - CNPq - Brazil (Nos. 450572/2009-9, 301973/2009-1 and 477268/2010-2). The author (MFAdaS) also acknowledges financial support from Financiadora de Estudos e Projetos - FINEP - Brazil (Ref. 2399/03). We also would like to acknowledge fruitful discussions with Dr. F.C. Mena.

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Observatoire de Paris-MeudonMeudon CedexFrance
  2. 2.Coordenação de Astronomia e Astrofísica, Observatório NacionalRio de JaneiroBrazil
  3. 3.Departamento de Física Teórica,Instituto de FísicaUniversidade do Estado do Rio de JaneiroRio de JaneiroBrazil
  4. 4.Sorbonne Université, UPMC Université Paris 06, LERMA, UMRS8112 CNRSParisFrance
  5. 5.School of Mathematical Sciences, Queen MaryUniversity of LondonLondonUK

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